In this section, we set up our notations and conventions for our model of the 3-form field \(\Omega = \Omega _{\mu \nu \rho }\,dx^\mu \wedge dx^\nu \wedge dx^\rho \) . In the fundamental theories such as the Type-IIA superstring theory or the HUFT, \(\Omega \) , as a gauge field, couples universally to other fields or particles. However, these fundamental theories are generically living in the spacetime with dimensions higher than 4. In order to explain the physics of our ordinary 4-dimensional spacetime world, one usually involves the compactification technique to wrap the extra dimensions in small compact spaces [1]}, [2]}, [3]}. In this process, due to the wavefunctions of various fields in the extra dimensional space, the couplings of \(\Omega \)  with the SM particles can become non-universal. Here we concentrate on the following 3-form field coupling to the SM muon leptons [4]}, [5]}, [6]} Note that, in Eq. (REF ), the convention for the \(\Omega \)  coupling \(g_h\)  to muons differs from that given in Fig. 4 of Ref. [5]} by a factor \(1/4\) .
\({\cal L}_\Omega \supset -\frac{1}{2\cdot 4!} \Omega ^{\mu \nu \rho \sigma } \Omega _{\mu \nu \rho \sigma }- \frac{m_\Omega ^2}{2\cdot 3!} \Omega _{\mu \nu \rho } \Omega ^{\mu \nu \rho } - i g_h \bar{\mu } \gamma ^{\mu \nu \rho } \mu \Omega _{\mu \nu \rho }\,,\) 
